Abstract
Throughout this paper, T is a ring with identity and F is a unitary left module over T. This paper study the relation between semihollow-lifting modules and semiprojective covers. proposition 5 shows that If T is semihollow-lifting, then every semilocal T-module has semiprojective cover. Also, give a condition under which a quotient of a semihollow-lifting module having a semiprojective cover. proposition 2 shows that if K is a projective module. K is semihollow-lifting if and only if For every submodule A of K with K/( A) is hollow, then K/( A) has a semiprojective cover.
Highlights
Let T be a ring with identity and F a unitary left module over T
Module F is called small on F (E ≪ F) if whenever a submodule S of J with F = E + S implies S = F 1
A submodule E of an T-module F is called semismall in F (E ≪S F) if E = 0 or E/V ≪ F/V for every nonzero submodule V of E 2
Summary
Let T be a ring with identity and F a unitary left module over T. Module F is called small on F (E ≪ F) if whenever a submodule S of J with F = E + S implies S = F 1. A submodule E of an T-module F is called semismall in F (E ≪S F) if E = 0 or E/V ≪ F/V for every nonzero submodule V of E 2.
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